Re: [中學] 分項對消法

[mack (腦海裡依然記得妳)]

※ 引述《t6370345 (貓咪QQ)》之銘言：
: ___1_____  + ____1_____  =
: 2*3*4*5       3*4*5*7
: 想請問這題限制使用分項消除的話該怎麼做呢?
: 謝謝
  1/(2*3*4*5) + 1/(3*4*5*6)
= (1/3) * [1/(2*3*4) - 1/(3*4*5)] + (1/3) * [1/(3*4*5) - 1/(4*5*6)]
= (1/3) * [1/(2*3*4) - 1/(4*5*6)]
= (1/3) * (1/2) * {[1/(2*3) - 1/(3*4)] - [1/(4*5) - 1/(5*6)]}
= (1/3) * (1/2) * [1/(2*3) - 1/(3*4) - 1/(4*5) + 1/(5*6)]
= (1/3) * (1/2) * [(1/2 - 1/3) - (1/3 - 1/4) - (1/4 - 1/5) + (1/5 - 1/6)]
= (1/3) * (1/2) * (1/2 - 2/3 + 2/5 - 1/6)
= (1/3) * (1/2) * [(15-20+12-5)/30]
= (1/3) * (1/2) * (2/30)
= 1/90

  1/(2*3*4*5) + 1/(3*4*5*6)
= [1/(3*4*5)] * (1/2 + 1/6)
= 1/(3*4*5) * (8/2*6)
= 8/(2*3*4*5*6)
= 1/(3*5*6)
= 1/90 ...何樂不為

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◆ From: 111.252.208.40
→ mack        :這應該是題目要的  可是分項有了  沒消除阿
→ mack        :個人不推這方法  提公因數更快
※ 編輯: mack            來自: 111.252.208.40       (11/21 10:20)
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